Abstract

We obtain infinite products related to the concept of visible from the origin point vectors. Among these is k=3(1Z)φ,(k)/k=11Zexp(Z32(1Z)212Z12Z(1Z)),|Z|<1, in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a,b,k)=1 where a<b<k, assuming (a,b,k) is the gcd(a,b,k).